Bioimpedance methods and apparatus

ABSTRACT

Methods and apparatus for providing bioimpedance analysis are provided. In certain aspects, equivalent circuit frequency response models are provided which lead to improved correlations with MRI data. The frequency response models take account of body composition, including the fat component of a body segment. Data obtained by performing bioimpedance spectroscopy (BIS) and MRI on the calves of subjects illustrates the improved correlations achieved compared to single frequency analyses at 50 kilohertz and analyses performed using the conventional Cole-Cole model.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase under 35 USC §371 ofInternational Application No. PCT/US2004/29711, filed Sep. 10, 2004,which was published in English under PCT Article 21(2) on Mar. 31, 2005as International Publication No. WO 2005/027717.

FIELD OF THE INVENTION

This invention relates to bioimpedance methods and apparatus and, moreparticularly, to the use of such methods and apparatus to determine themuscle content, fat content, and/or extracellular fluid content of asegment of the body of a subject, where a segment can includeessentially the subject's entire body.

BACKGROUND OF THE INVENTION

The electrical properties of biologic tissue has been of scientificinterest for a substantial period time. Many developments and newdevices based on a knowledge of bioelectricity have been used in biologyand the biomedical area in the last century.

Bioelectrical impedance analysis is one of the interesting andchallenging subjects in this area. Bioimpedance has been studied in manyareas of medicine because of its potential ability to measure bodycomposition with noninvasive, simple, inexpensive, and portable methods.In particular, bioimpedance has been employed in clinical research formany years. For example, clinical applications using bioimpedance werereported at an early stage by Nyboer [3] and Patterson [4].

Many authors have investigated the nature of the electrical propertiesof living tissue [2, 4, 5]. Schwan et al. described the relationshipbetween the dielectric properties of the cell membrane usingmulti-frequency currents [2]. A basic theory to explain electricalproperties of tissue in the body has been well established by Cole [1].In particular, Cole successfully developed an equivalent circuit model(hereinafter the “Cole-Cole model”) to explain the electrical responseof cells and their membranes to AC current.

A method of using bioimpedance spectroscopy (BIS) has been suggested tomeasure extracellular (ECV) and intracellular (ICV) fluid volumes basedon the Cole-Cole model and the Hanai method [5, 6, 10]. The methodologyof multi-frequency bioimpedance analysis can now provide someinformation about extracellular and intracellular fluid volume in thetotal or segmental body compartment [6].

However, the accuracy of bioimpedance analysis, including BIS, is amajor point of concern by the clinical user [7, 8]. Even though manystudies have reported the use of bioimpedance analysis to estimate bodyfluids, the current techniques have not been accepted widely in clinicalpractice because of questions regarding reliability, validity, andaccuracy.

There are many factors which adversely affect the accuracy of themeasurement and analysis using currently available bioimpedancetechniques. In accordance with certain of its aspects, the presentinvention is concerned with one of those factors, namely, the model usedto analyze bioimpedance data. The bioimpedance model commonly used todate to calculate electrical properties of different tissues has a basicassumption that fat has a high resistivity compared to fat free mass,and that therefore, fat mass can be ignored. However, a recent studyfound that bioimpedance measurements at 50 kilohertz are affected whensubjects have large amounts of adipose tissue [7]. As discussed indetail below, in accordance with the present invention it has been foundthat the amount of fat mass is one of the major factors affecting theaccurate measurement of body composition by BIS for subjects having avariety of body mass index (BMI) values.

SUMMARY OF THE INVENTION

In accordance with a first aspect, the invention provides a method foranalyzing bioimpedance data for a body segment of a subject, said bodysegment having an external skin surface, said method comprising:

(a) applying alternating current at a plurality of frequencies to atleast two points on the external skin surface so as to cause current topass through the segment;

(b) for each frequency, recording the voltage difference between atleast two other points on the external skin surface, said recordedvoltage differences comprising both magnitude and phase information(i.e., magnitude and phase values or, equivalently, resistance andreactance values); and

(c) using the recorded voltage differences at the plurality offrequencies to determine at least one numerical value indicative of themuscle, fat, and/or extracellular fluid content of the segment, saidnumerical value being determined using an impedance model for thesegment which at least comprises three parallel paths, one of whichconsists of a capacitor C_(M) and a resistor R_(I) in series whichrepresent primarily the muscle component of the segment, one of whichconsists of a capacitor C_(F) and a resistor R_(F) in series whichrepresent primarily the fat component of the segment, and one of whichconsists of a resistor.

In accordance with a second aspect, the invention provides a method foranalyzing bioimpedance data for a body segment of a subject, said bodysegment having an external skin surface, said method comprising:

(a) applying alternating current at a plurality of frequencies to atleast two points on the external skin surface so as to cause current topass through the segment;

(b) for each frequency, recording the voltage difference between atleast two other points on the external skin surface, said recordedvoltage differences comprising both magnitude and phase information(i.e., magnitude and phase values or, equivalently, resistance andreactance values); and

(c) using the recorded voltage differences at the plurality offrequencies to determine at least one numerical value indicative of thefat and/or extracellular fluid content of the segment, said numericalvalue being determined using an impedance model for the segment which atleast comprises two parallel paths, one of which consists of a capacitorC_(F) and a resistor R_(F) in series which represent primarily the fatcomponent of the segment and the other of which consists of a resistorwhich primarily represents the extracellular fluid component of thesegment;

wherein:

(i) the two parallel paths are the only parallel paths of the impedancemodel which represent the composition of the segment internal to theskin; and

(ii) each of the frequencies applied in step (a) is less than or equalto 10 kilohertz.

In accordance with certain embodiments of the foregoing aspects of theinvention, a correlation equation is used which transforms a modelparameter (e.g., R_(F)) to a physiological value (e.g., a fat contentvalue) for the segment. The correlation equation can be obtained by:

(i) performing steps (a), (b), and (c) on a plurality of calibrationsubjects to obtain a model parameter value for each of said subjects;

(ii) performing a measurement on the segment for the plurality ofcalibration subjects (e.g., a measurement of fat content using magneticresonance imaging) to obtain a physiological value for the segment foreach of said subjects; and

(iii) performing a regression analysis on the values obtained in steps(i) and (ii) to obtain the correlation equation.

Preferably, the plurality of calibration subjects includes at least onesubject having a body mass index less than 20 and at least one subjecthaving a body mass index greater than 35. More preferably, the pluralityof calibration subjects includes at least one subject having a body massindex less than 20 and at least one subject having a body mass indexgreater than 40.

In accordance with a third aspect, the invention provides a method fordetermining the circumference of a portion of a body segment covered byskin comprising:

(a) applying a series of electrodes around said portion, said series ofelectrodes having a first electrode and a last electrode, thecircumferential distances between all electrodes in the series beingknown, except for the distance between the first and last electrodes;

(b) determining the resistance between at least two electrodes of theseries, other than the first and last electrode, by applying a lowfrequency current which does not substantially penetrate the skin;

(c) determining a resistivity value per unit length for the skin fromthe resistance determined in step (b) and the known circumferentialdistance between the two electrodes;

(d) determining the resistance between the first and last electrodes ofthe series by applying a low frequency current which does notsubstantially penetrate the skin; and

(e) calculating the distance between the first and last electrodes ofthe series from the resistance measured in step (d) and the resistivityvalue per unit length determined in step (c).

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary of theinvention, and are intended to provide an overview or framework forunderstanding the nature and character of the invention.

Additional features and advantages of the invention are set forth in thedetailed description which follows, and in part will be readily apparentto those skilled in the art from that description or recognized bypracticing the invention as described herein. The accompanying drawingsare included to provide a further understanding of the invention, andare incorporated in and constitute a part of this specification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a body composition model in accordance with the invention,both in cross-sectional form (FIG. 1A) and three-dimensional form (FIG.1B).

FIGS. 2A and 2B are equivalent circuit frequency response models for thebody composition model of FIG. 1.

FIG. 3 is an equivalent circuit frequency response model for the bodycomposition model of FIG. 1 under low frequency conditions, e.g.,frequencies less than 10 kilohertz.

FIG. 4 shows an electrode configuration that can be used in the practiceof the invention.

FIG. 5 shows a resistor model for the electrode configuration of FIG. 4.

FIG. 6 shows the electrode placement used to generate the bioimpedancedata of the examples presented below.

FIG. 7 shows correlations between measured and calculated ρ valuesobtained using Equations 12 and 13. The steeper slope of the correlationobtained using Equation 12 illustrates the value of includinginformation regarding fat content in equivalent circuit frequencyresponse models for bioimpedance measurements.

FIG. 8 shows p values of a t-test between groups of subjects havingdifferent fat contents.

FIG. 9 shows curve fitting of impedance for three subjects (patients)having different fat contents.

FIG. 10 shows impedance magnitude (FIG. 10A) and impedance phase (FIG.10B) for a subject (patient) with a 0.588 kg fat mass.

FIG. 11 shows impedance magnitude (FIG. 11A) and impedance phase (FIG.11B) for a subject (patient) with a 0.134 kg fat mass.

FIG. 12 shows a correlation between muscle (MS) estimation by MRI and bya BIS technique of the invention.

FIG. 13 shows a correlation between muscle mass measured by MRI andresistance measured at 5 kHz.

FIG. 14 compares (i) a correlation between muscle mass measured by MRIand intracellular resistance (R_(I)) determined using themulti-frequency, three parallel path model of the invention (FIG. 14A)with (ii) a correlation between muscle mass measured by MRI andimpedance at 50 KHz (FIG. 14B).

FIG. 15 compares (i) a correlation between fat mass measured by MRI andfat resistance (R_(F)) determined using the multi-frequency, threeparallel path model of the invention (FIG. 15A) with (ii) a correlationbetween fat mass measured by MRI and impedance at 50 KHz (FIG. 15B).

FIG. 16 compares (i) a correlation between muscle mass measured by MRIand intracellular resistance (R_(I)) determined using themulti-frequency, three parallel path model of the invention (FIG. 16A)with (ii) a correlation between muscle mass measured by MRI andintracellular resistance determined using the Cole-Cole model (FIG.16B).

FIG. 17 compares (i) a correlation between fat mass measured by MRI andfat resistance (R_(F)) determined using the multi-frequency, threeparallel path model of the invention (FIG. 17A) with (ii) a correlationbetween fat mass measured by MRI and intracellular resistance determinedusing the Cole-Cole model (FIG. 17B).

DETAILED DESCRIPTION OF THE INVENTION AND ITS PREFERRED EMBODIMENTS

As discussed above, the present invention relates to bioimpedancemethods and apparatus which can provide information regarding the fat,muscle, and/or extracellular fluid content of a segment of a body of asubject, i.e., a human or an animal.

The segment will typically be a part or all of a subject's limb, e.g., asubject's calf or forearm, but can also be all or part of the subject'storso, e.g., part or all of the subject's abdomen. Similarly, thesegment can be as small as a specific muscle or a part of a muscle andas large as essentially the subject's entire body.

The location and size of the segment will depend on the placement ofcurrent applying electrodes on the subject's skin. In particular, thesegment will constitute the portion of the subject's body through whichsubstantial current passes when the current applying electrodes areactivated. By suitable choices of the number, location, and polarity ofthe current applying electrodes, a variety of current patterns withinthe subject's body can be achieved. Indeed, by varying the polarity ofselected current applying electrodes, more than one segment can beanalyzed without the need to move the current applying electrodes.

As known in the art, the potential recording electrodes will typicallybe located inboard of the current applying electrodes, i.e., thepotential recording electrodes will typically be located on skin whichsurrounds the portion of the patient's body through which substantialcurrent passes when the current applying electrodes are activated.

The application of current and the recording of potentials can beperformed with bioimpedance equipment, including current applying andrecording electrodes, now known or subsequently developed, e.g.,commercially available equipment such as the 4000B Bio-ImpedanceSpectrum Analyzer System (Xitron Technologies, Inc., San Diego, Calif.)used in the examples discussed below. Alternatively, customizedequipment can be used in the practice of the invention.

Processing of the data obtained by the bioimpedance equipment can beperformed entirely within the equipment or can be performed on-lineusing a separate computer. Alternatively, the data can be stored andprocessed subsequent to the time of measurement.

Preferably, the bioimpedance equipment will include a microprocessorprogrammed to perform at least a portion of the analysis procedures ofthe present invention. For example, the bioimpedance equipment can applya regression equation obtained from a study on calibration subjects tomeasured impedance data for a subject and thus directly report thesubject's fat, muscle, and/or extracellular fluid content(s) to the userof the equipment, e.g., the subject himself and/or other personnel,e.g., a health care provider, interested in the information. The fat,muscle, and/or extracellular fluid content can be reported graphically,numerically (e.g., as a fat and/or muscle percentage value), by color(e.g., red for high fat content), or the like.

In certain embodiments of the invention, alternating current at aplurality of frequencies is applied to the subject's skin. Preferably,at least 10 frequencies are used and more preferably, approximately 50frequencies are used. Preferably, the plurality of frequencies comprisesfrequencies between 5 and 1000 kilohertz, although frequencies overlarger or smaller ranges can be used if desired. Most preferably, thefrequencies are logarithmically distributed over the frequency range.

As discussed above, the bioimpedance model commonly used to date tocalculate electrical properties of different tissues has suffered from anumber of problems. One of those problems is the basic assumption thatfat has a high resistivity compared to fat free mass, and thattherefore, fat mass can be ignored. Another is related to the model'scalculation of extracellular and intracellular resistances. Although notaccounted for in the existing model, that model, which is based on thetissue under the skin, is influenced by the skin and amount of adiposetissue.

The present invention is directed to reducing various of the problemswith the present analysis approach by examining the response ofdifferent constituent body components, such as skin, fat, muscle, toelectrical input. More particularly, the invention, in accordance withcertain of its aspects, provides models to describe the effects ofdifferent components of body tissue using equivalent circuits.

Specifically, to improve current bioimpedance techniques, in accordancewith certain aspects of the present invention, an improved electricalmodel is provided which is able to explain the electrical propertieswith different proportions of body tissues, and the effect of a widerange of current frequencies. The data presented below in Example 1specifically evaluates the relationship of the resistivity at 5 kHzmeasured at the skin to the resistivity by calculation with the model.

FIG. 1 shows a segmental body composition model in accordance with theinvention which can be used to describe the components of conductivityin the limbs. In particular, the figure shows conductive components in alimb segment which form the basis for the electrical models of theinvention. For reference, Table 1 shows the electrical properties(permittivity and resistivity) of different tissues using a 10 kHzcurrent frequency as reported in a previous study [8].

An equivalent circuit model to FIG. 1 is shown in FIG. 2A, where R_(G)represents resistance of measurement by two electrodes on the skin andR_(S), R_(F), R_(E), R_(I), and R_(B) represent resistance of the skin,fat mass, extracellular volume, intracellular volume, and bone,respectively. In FIG. 2A, C_(IN), C_(F), and C_(M) represent capacitancebetween skin and electrode, capacitance of fat mass, and capacitance ofmembrane of cells, respectively.

From the model in FIG. 2A, the total electrical current (I_(G)) can begiven by:I _(G) =I _(S) +I _(F) +I _(E) +I _(I) +I _(B)  Eq. 1

Potential across R_(G) can be obtained by:

$\begin{matrix}{{R_{G}I_{G}} = {{R_{E}I_{E}} + \frac{2\; I_{G}^{\prime}}{\omega\; C_{IN}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where I′_(G) is the current pass through capacitor C_(IN), and is givenby:I′ _(G) =I _(F) +I _(E) +I _(I) +I _(B)  Eq. 3

Because skin resistance (R_(S)) is much higher than in other tissueI_(S) is very low, so that we have:I′_(G)≈I_(G)  Eq. 4

Since current at low frequency (e.g., 5 kHz) will not pass through theintracellular space, the equivalent circuit can be modified as shown inFIG. 3.

In FIG. 3, E represents the potential between two measuring electrodes(across R_(G)) and E_(E) represents the potential across R_(E).Therefore, the following potential equation can be written:

$\begin{matrix}{E = {E_{E} + \frac{2\; I_{G}}{{j\omega}\; C_{IN}}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$where the parameter

$\frac{2\; I_{G}}{{j\omega}\; C_{IN}}$represents the potential across the capacitor C_(IN). This potential canbe ignored at high current frequency or when C_(IN) is large.

According to the parallel circuit of FIG. 3, the resistance R_(G) ofmeasurement from skin electrodes can be calculated by:

$\begin{matrix}{R_{G} = {\frac{R_{E}\left( {\frac{1}{{j\omega}\; C_{F}} + R_{F}} \right)}{R_{E} + \frac{1}{{j\omega}\; C_{F}} + R_{F}} + \frac{2}{{j\omega}\; C_{IN}}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

Reactance of fat mass (X_(F)) and reactance between skin and electrode(X_(IN)) are as follows:

${X_{F} = {- \frac{j}{\omega\; C_{F}}}},{X_{IN} = {- \frac{j}{\omega\; C_{IN}}}}$

Thus, R_(G) can be simplified to:

$\begin{matrix}{{R_{G} = {{R_{E}\left( {1 + \frac{R_{E}/X_{F}}{1 + {\left( {R_{E} + R_{F}} \right)/X_{F}}}} \right)} - {2X_{IN}}}}{and}} & {{Eq}.\mspace{14mu} 7} \\{R_{G} = {{R_{E}\left( {1 + \frac{A_{F}}{\left. {{\frac{\rho_{F}}{\rho_{E}}A_{E}} + A_{F}} \right)}} \right)} - {2X_{IN}}}} & {{Eq}.\mspace{14mu} 8}\end{matrix}$where A_(F) and A_(E) represent the cross sectional area of fat massfrom MRI and ECV in this segment, respectively. According to a previousstudy, the ratio of resistivity in fat mass to resistivity in ECV isapproximately as follows [6].

$\begin{matrix}{\frac{\rho_{F}}{\rho_{E}} \approx {3 - 5}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$

Equation 8 can be further simplified to:

$\begin{matrix}{\rho_{G} = {{\rho_{E}\frac{A_{G}}{A_{E}}\left( {1 + \frac{A_{F}}{A_{G}}} \right)} - {2X_{IN}\frac{A_{G}}{L}}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$where ρ_(G) is the resistivity measured on the skin and ρ_(E) is theresistivity in ECV space with a constant value. Letting

$\begin{matrix}{k_{E} = \left( {1 + \frac{A_{F}}{A_{G}}} \right)} & {{Eq}.\mspace{14mu} 11}\end{matrix}$and assuming that

$2X_{IN}\frac{A_{G}}{L}$is small, we have:

$\begin{matrix}{\rho_{G,{Cal}} = {k_{E}\rho_{E}\frac{A_{G}}{A_{E}}}} & {{Eq}.\mspace{14mu} 12}\end{matrix}$

If k_(E)=1, resistivity can be calculated by:

$\begin{matrix}{\rho_{G,{Cal}}^{*} = {\rho_{E}\frac{A_{G}}{A_{E}}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

The application of these equations and, in particular, Equations 12 and13 to experimental data obtained from a set of calibration subjects isset forth below in Example 1. The results described therein indicatethat the volume of fat mass is an important factor influencing theestimation of body composition using the standard four-electrodebioimpedance technique.

The experimental data of Example 1 was obtained using one frequency forthe applied current, namely, 5 kilohertz. The invention's equivalentcircuit models of segmental body components are preferably used todescribe responses to multi-frequency current. Example 2 shows theresults of such multi-frequency testing. In particular, this exampleshows different decreases in impedance with increases in currentfrequency for subjects with different fat contents.

FIG. 2B is a modified version of the equivalent circuit model of FIG.2A. In FIG. 2B, Z_(Total) represents total impedance of measurement bytwo electrodes at A and B. As in FIG. 2A, R_(S), R_(F), R_(E), R_(I),and R_(B) represent resistance of the skin, fat mass, extracellular andintracellular volume, and bone, respectively, and C_(IN), C_(F), andC_(M) represent capacitance between skin and electrode, capacitance offat mass and the capacitance of the membranes of the cells,respectively. R_(i1) and R_(i2) represent resistance of segmental bodybetween injecting and measuring electrodes.

To obtain a relationship based on frequency for the model of FIG. 2,equations were used to simplify the model so that it can bestandardized. First, we let R_(P) represent the parallel resistance ofR_(E) and R_(B):

$\begin{matrix}{R_{P} = \frac{R_{E} \times R_{B}}{R_{E} + R_{B}}} & {{Eq}.\mspace{14mu} 14}\end{matrix}$Secondly, we used the following parameters a, b, c, and d to simplifythe calculation:a=R_(I)R_(F)C_(I)C_(F)  Eq. 15b=C _(I) C _(F)(R _(I) +R _(F))  Eq. 16c=C_(F)C_(I)  Eq. 17d=C _(F) +C _(I)  Eq. 18

Total impedance (Z_(Total)) can be obtained from the circuit of FIG. 2and is given by the following Eq. 19:

$\begin{matrix}{Z_{Total} = \frac{\begin{matrix}{{{aC}_{IN}R_{P}{R_{S}({j\varpi})}^{3}} + {{R_{S}\left\lbrack {{\left( {2 + C_{IN}} \right){bR}_{P}} + {2a}} \right\rbrack}({j\varpi})^{2}} +} \\{R_{S}\left\lbrack {{\left( {{C_{IN}{cR}_{P}} + {2b} + {2{dRp}}} \right\rbrack({j\varpi})} + {2{cR}_{S}}} \right.}\end{matrix}}{\begin{matrix}{{{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack}({j\varpi})^{3}} +} \\{{\left\lbrack {{R_{S}{C_{IN}\left( {{dR}_{P} + b} \right)}} + {{bR}_{P}\left( {2 + C_{IN}} \right)} + {2a}} \right\rbrack({j\varpi})^{2}} +} \\{{\left\lbrack {{{cR}_{S}C_{IN}} + {\left( {{cC}_{IN} + {2d}} \right)R_{P}} + {2b}} \right)({j\varpi})} + {2c}}\end{matrix}}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$

To standardize Eq. 19, we letμ=C _(IN) [R _(S)(a+bR _(P))+aR _(P)]  Eq. 20

Z_(Total) is then given by Eq. 21 as follows:

$\begin{matrix}{Z_{Total} = \frac{\begin{matrix}{{\left( \frac{1}{\mu} \right){aC}_{IN}R_{P}{R_{S}({j\varpi})}^{3}} +} \\{{\frac{1}{\;\mu}{R_{\; S}\left\lbrack {{\left( {2 + C_{\;{IN}}} \right){bR}_{\; P}} + {2a}} \right\rbrack}({j\varpi})^{2}} +} \\{\frac{R_{S}}{\mu}\left\lbrack {{\left( {{C_{IN}{cR}_{P}} + {2b} + {2{dRp}}} \right\rbrack({j\varpi})} + \frac{2{cR}_{S}}{\mu}} \right.}\end{matrix}}{\begin{matrix}{({j\varpi})^{3} + {\frac{1}{\mu}\left\lbrack {{R_{S}{C_{IN}\left( {{dR}_{P} + b} \right)}} +} \right.}} \\{{\left. {{{bR}_{P}\left( {2 + C_{IN}} \right)} + {2a}} \right\rbrack({j\varpi})^{2}} +} \\{{\left. {\frac{1}{\mu}\left\lbrack {{{cR}_{S}C_{IN}} + {\left( {{cC}_{IN} + {2d}} \right)R_{P}} + {2b}} \right)} \right\rbrack({j\varpi})} + \frac{2c}{\mu}}\end{matrix}}} & {{Eq}.\mspace{14mu} 21}\end{matrix}$

Quantitative analysis of frequency response data for individual subjectsis preferably performed using a group of parameters to represent thefunction of components in the equivalent circuit. Such a group ofparameters helps in the identification of differences in the bodycomposition of individual subjects by facilitating the use of a standardtransfer function for the analysis.

Equation 21 can, for example, be normalized using the followingrelationship, where P₁, P₂, P₃, P₄, Q₁, Q₂, Q₃ are the group ofparameters:

$\begin{matrix}{Z_{Total} = {\frac{{P_{1}({j\varpi})}^{3} + {P_{2}({j\varpi})}^{2} + {P_{3}({j\varpi})} + P_{4}}{({j\varpi})^{3} + {Q_{1}({j\varpi})}^{2} + {Q_{2}({j\varpi})} + Q_{3}}.}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

Values for R_(I), R_(F), C_(I), C_(F), R_(P), R_(S), C_(IN) forindividual patients (individual subjects) are calculated using thefollowing equations:

$\begin{matrix}\begin{matrix}{P_{1} = {{\left( \frac{1}{\mu} \right){aC}_{IN}R_{P}R_{S}} = \frac{{aC}_{IN}R_{P}R_{S}}{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right.}}} \\{= \frac{{aR}_{P}R_{S}}{{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}}}\end{matrix} & {{Eq}.\mspace{14mu} 23} \\{P_{2} = {{\frac{1}{\mu}{R_{S}\left\lbrack {{\left( {2 + C_{IN}} \right){bR}_{P}} + {2a}} \right\rbrack}} = \frac{R_{S}\left\lbrack {{\left( {2 + C_{IN}} \right){bR}_{P}} + {2a}} \right\rbrack}{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 24} \\{P_{3} = {{\frac{R_{S}}{\mu}\begin{bmatrix}{{C_{IN}{cR}_{P}} +} \\{{2b} + {2{dRp}}}\end{bmatrix}} = \frac{R_{S}\left\lbrack {{C_{IN}{cR}_{P}} + {2b} + {2{dRp}}} \right\rbrack}{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 25} \\{P_{4} = {\frac{2{cR}_{S}}{\mu} = \frac{2{cR}_{S}}{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 26} \\{Q_{1} = {{\frac{1}{\mu}\begin{bmatrix}{{R_{S}{C_{IN}\left( {{dR}_{P} + b} \right)}} +} \\{{{bR}_{P}\left( {2 + C_{IN}} \right)} + {2a}}\end{bmatrix}} = \frac{\begin{bmatrix}{{R_{S}{C_{IN}\left( {{dR}_{P} + b} \right)}} +} \\{{{bR}_{P}\left( {2 + C_{IN}} \right)} + {2a}}\end{bmatrix}}{C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 27} \\{Q_{2} = {{\frac{1}{\mu}\begin{bmatrix}{{{cR}_{S}C_{IN}} +} \\\left. {{\left( {{cC}_{IN} + {2d}} \right)R_{P}} + {2b}} \right)\end{bmatrix}} = \frac{\begin{bmatrix}{{{cR}_{S}C_{IN}} +} \\\left. {{\left( {{cC}_{IN} + {2d}} \right)R_{P}} + {2b}} \right)\end{bmatrix}}{C_{In}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{p}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 28} \\{Q_{3} = {\frac{2c}{\mu} = \frac{2c}{\left. {C_{IN}\left\lbrack {{R_{S}\left( {a + {bR}_{P}} \right)} + {aR}_{P}} \right\rbrack} \right\rbrack}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$where a, b, c, and d are as defined above in Equations 15-18.

In these equations, R_(I), R_(F), C_(I), C_(F), R_(P), R_(S), C_(IN) arethe variables to be determined and P₁, P₂, P₃, P₄ Q₁, Q₂, Q₃ are datavalues for an individual patient obtained by curve fitting of thefrequency response data for the patient. In particular, the values ofthe seven variables R_(I), R_(F), C_(I), C_(F), R_(P), R_(S), C_(IN) foran individual patient are obtained by solving the above seven equations(Eq. 23 to Eq. 29) using the P₁, P₂, P₃, P₄ Q₁, Q₂, Q₃ values for thatpatient.

In Example 2 below, the curve fitting program of the MATLAB toolbox (TheMathWorks, Inc., Natick, Mass.) was used to obtain the values of theparameters P₁, P₂, P₃, P₄, Q₁, Q₂, Q₃ for individual patients.Simulation of frequency response curves was obtained using the standardsignal processing program of the MATLAB toolbox.

Although Eq. 22 is a preferred curve fitting equation for use with thetype of frequency response data obtained during a bioimpedanceexperiment, as will be evident to persons skilled in the art from thepresent disclosure, other curve fitting equations can be used ifdesired. Similarly, other math processing programs besides the MATLABprograms can be used in the practice of the invention.

Segmental length and circumference can be measured manually.Alternatively, in accordance with certain embodiments of the invention,the circumference and the length of a segment can be measured usinggroups of electrodes instead of single electrodes (see FIG. 4). Theresistance at low frequency (e.g., <10 Hz, preferably <1 Hz) can reflectthe electrical properties of the skin. Since the distance between anyadjacent two electrodes in each pair is known, the circumference of themeasurement area can be calculated as,

$\begin{matrix}{C = {{D \cdot \left( {n - 1} \right)} + \frac{R_{n}}{\lambda}}} & {{Eq}.\mspace{14mu} 30}\end{matrix}$where C represents the circumference, n is the number of electrodes, Dis a known distance between two adjacent electrodes, R_(n) (n=8 in FIG.5) is the resistance between the first and last electrode when theelectrodes form a circle on any segment, and λ is the ratio ofresistivity to the area of cross sectional area which can be calculatedby

$\begin{matrix}{\lambda = {\frac{1}{n - 1}{\sum\limits_{i = 1}^{n - 1}\;\frac{R_{i}}{D_{i}}}}} & {{Eq}.\mspace{14mu} 31}\end{matrix}$where R_(i) is the resistance between any adjacent two electrodes exceptthe resistance between the first and end, D_(i) is the distance betweenany adjacent two electrodes except the distance between the first andthe last electrodes.

Thus, specific resistivity in skin of this segment isρ′=λ×A  Eq. 32where A is the cross sectional area in the segment. Since A=C²/(4*π), ρ′can be calculated byρ′=λ*C ²/(4*π)  Eq. 33Once the skin resistivity is determined, the length can be calculated bythe equationL=A*R _(L)/ρ′  Eq. 34where L is the length and A is the cross sectional area of the segmentand R_(L) is the resistance between two cross sectional areas along thevertical axis of the segment.

In FIG. 4, E1 to E8 are electrodes, D1 to D7 represent the distancebetween two adjacent electrodes respectively, and D1=D2= . . . =D7. InFIG. 5, R1 to R7 represents the skin resistance between adjacent twoelectrodes. R8 is the resistance between, as discussed above, the first(E1) and the last electrode (E8). The distance between E1 and E8 isunknown but it, as discussed above, can be calculated by R8/λ andtherefore, the circumference (C) can be calculated by Eq. 30.

The mathematical operations described herein can be performed using avariety of computers and software. For example, those operations can beperformed using the commercially available MATLAB program discussedabove and a personal computer configured to run that program inaccordance with the program manufacturer's specifications. The programas customized to perform the mathematical operations of the inventioncan be embodied as an article of manufacture comprising a computerusable medium, such as a magnetic disc, an optical disc, or the like,upon which the program is encoded. The data generated by the programscan similarly be stored on various types of storage media.

Without intending to limit it in any manner, the present invention willbe more fully described by the following examples.

Example 1 Effect of Fat Mass on Bioimpedance Analysis

This example shows that fat mass is a major factor affecting theaccurate measurement of body composition, including the accuratemeasurement of body fluid in clinical practice in dialysis patients,using bioimpedance analysis.

28 chronic hemodialysis patients were studied before treatment. Table 2sets forth the relevant parameters for this group of subjects(patients).

Calf bioimpedance measurements were performed using BIS device Xitron4200 (Xitron Technologies, San Diego, Calif.). The procedure ofplacement of electrodes was published in a previous study [9]. Asdescribed therein, to place the electrodes in the normal position, thedistance (H) between the central part of the patella and the center ofthe lateral malleolus was measured while the subject was in the sittingposition (see FIG. 6). With the patient recumbent, two measuringelectrodes were placed, one 5 cm above the mid point M and another 5 cmbelow. Two current injecting electrodes were placed, one 3 cm above andthe other 3 cm below the measuring electrodes. The circumference of thecalf at the two measuring electrodes was measured using a tape with 0.1cm precision.

Calf resistance and reactance were measured using the BIS device with 50logarithmically distributed frequencies from 5 kHz to 1 MHz.Extracellular resistance (Re) and intracellular resistance (Ri) werecalculated and ECV and ICV were obtained using a program provided by theBIS device [9, 10]. Fat mass, muscle mass, and bone were separatelymeasured in the same area by MRI.

Geometric volume (V_(G)) was defined as the cross sectional area (A_(G))times the length (L) of the segment. A_(G) can be calculated byA_(G)=C²/(4π), where C is average value of circumferences in the calf.Resistivity (ρ_(G,Mea)) was calculated by the value of measurement shownas follows:

$\begin{matrix}{\rho_{G,{Mea}} = \frac{R_{G} \times A_{G}}{L}} & {{Eq}.\mspace{14mu} 35}\end{matrix}$where R_(G) is resistance measured at 5 kHz, A_(G) is cross sectionalarea and length was fixed at 10 cm for all subjects.

In order to compare the effect of volume of fat mass on the value ofresistivity from both measurement and calculation, the 28 patients weredivided into two groups according to the ratio of fat mass (V_(F)) togeometric volume (V_(G)): the high fat group was defined asV_(F)/V_(G)>0.2 and the normal fat group was defined as V_(F)/V_(G)≦0.2.Data is presented as mean value±SD, and the student t-test was used tocompare the data from different groups. A difference between groups wasconsidered significant if the p value<0.05.

Table 3 shows results of comparison of the resistivity between the twogroups. There were significant differences in ρ_(G,Mea) (p<0.05),ρ_(G,Cal) (p<0.005) and Δρ (p<0.05), however, no significant differencewas seen in ρ*_(G,Cal) between the two groups (Table 3). The difference(p<0.05) between ρ_(G,Mea) and ρ*_(G,Cal) was significant but nosignificant difference was seen between ρ_(G,Mea) and ρ_(G,Cal).

FIG. 7 shows correlations between calculated and measured resistivityvalues using Equations 12 and 13. The figure shows a high degree ofcorrelation between the resistivity (ρ_(G,Mea)) determined from Eq. 35which is based on the measured value and the resistivity (ρ_(G,Cal))calculated using Eq. 12. In FIG. 7, the diamond symbols represent thecorrelation of ρ_(G,Mea) with ρ*_(G,Cal) by Eq. 13(ρ*_(G,Cal)=0.66ρ_(G,Mea)+76.7, R²=0.96) and the symbols of solidcircles represent the correlation between ρ_(G,Mea) and ρ_(G,Cal) withindividual various k_(E) calculated by Eq. 12(ρ_(G,Cal)=0.93ρ_(G,Mea)+41.1, R²=0.9). Even though the correlation ishigh between ρ*_(G,Cal) and ρ_(G,Mea), the slope (diamond symbol) isonly 0.66. After calibration with individual k_(E) using Eq. 12, theslope is 0.93 (solid circles), i.e., significantly better.

Knowledge of the relationship of resistivity measured at the skin to thevarious subcutaneous tissues is essential to understand the relevantbioelectric phenomena. Many early studies have shown the resistivity ofvarious biologic tissues and organs by direct measurement [6]. However,since clinical measurements are performed on the surface of skin and theresistivity of different tissues is calculated by a number oftheoretical models, errors may occur due to: (1) individual differentimpedance interfaces of electrode and skin; (2) different volumes ofadipose tissue between individuals and (3) theoretical models that donot include the variables of differences in skin impedance and fat massbetween individuals.

The present invention provides a model which includes the variable ofimpedance of fat mass and may include the variables of resistance ofskin and interface between capacitance. Table 3 shows that there issignificant difference in resistivity (Δρ) at 5 kHz between calculationby the model and by measurement as the amount of fat mass increases.This suggests that the value of resistivity at low frequency (5 kHz)obtained from measurement on the skin should include the contributionnot only from extracellular fluid compartment but also from the fat masscompartment. FIG. 7 shows that after calibration with individual k_(E)the slope of the curve as shown by the solid circles is almost equal toone, which indicates that the calculated value is close to themeasurement values. It is important to understand that the variabilityof resistivity in healthy subjects depends mainly on the individualvolume of fat mass. Therefore using this model, correct informationconcerning ECV can be obtained by measurement of, for example, calfresistivity. This information is important to provide, among otherthings, an accurate parameter of hydration for adjusting the variablyabnormal hydration in dialysis patients; this will permit targetingappropriate body weight by removal of excess body fluid during dialysis.

In summary, this example illustrates some of the aspects of theinvention that provide a model which can be used as a basis to calculatethe resistivity in different tissues from the measurement of resistivityat the skin surface. That is, this example illustrates some of theaspects of the invention that provide an electrical resistivity model ofsegmented body composition for use in bioimpedance analysis, where themodel describes the relationship of the resistivity with measurement onthe skin surface and by calculation of tissues composing a limb.

In particular, in this example, a specific analysis was performed in agroup of subjects with 5 kHz current injected at the surface of thecalf. The study showed that calculated resistivity using the model washighly correlated with the values of resistivity by actual measurement.In the next example, the response of the system to current of differentfrequencies is investigated. The results of that example show that theresistivity of cell membranes can be tested using the three parallelpath model of the invention.

Example 2 Multi-Frequency Analysis

To improve existing BIS techniques, a correct electrical model should beable to explain the electrical properties with different proportions ofbody tissues over a wide range of current frequencies. The aim of thisstudy was to evaluate frequency response of the equivalent circuit modelfrom 5 kHz to 1 MHz measured at the skin of the calf, The equivalentcircuit model is shown in FIG. 2B.

The same 28 chronic hemodialysis patients as in Example 1 were studiedbefore treatment (see Table 2). Again, calf bioimpedance measurementswere performed using BIS device Xitron 4200 (Xitron Technologies, SanDiego, Calif.) and the placement of electrodes was as described above inExample 1 (see FIG. 6).

Calf resistance and reactance were measured using BIS device with 50logarithmically distributed frequencies from 5 kHz to 1 MHz. Fat mass,muscle mass and bone were separately measured in the same area of BISmeasurement by MRI. Patients were divided into three groups according tothe amount of fat mass in the calf with G1: fat>0.4 kg, G2: 0.25<fat<0.4kg and G3: fat<0.25 kg.

Significant differences in resistance, reactance and impedance betweenG1 and G3 were found; however, the significant difference between G1 andG2 show only with frequencies higher than 40 kHz (FIG. 8). Results ofcurve fitting to the raw data (circle, triangle and square) of impedancewith different frequencies are shown in FIG. 9. The data shown bycircles is for a patient having a fat mass of 0.59 kg as estimated byMRI, while the triangles and squares show data for two other patientshaving fat masses of 0.29 kg and 0.23 kg, respectively, again estimatedby MRI.

The frequency response curve (A) and phase response (B) are shown inFIGS. 10 and 11 from two patients: one had 0.55 kg fat mass, 1.046 kgmuscle mass and 0.021 kg bone (FIG. 10) as estimated by MRI and theother had 0.134 kg fat mass, 1.022 kg muscle mass and 0.022 kg bone(FIG. 11), again estimated by MRI.

It is clearly observed that impedance of the patient with smaller fatmass decreases in the range of frequency from 1 to 10 kHz (FIG. 11A),however, the curve is almost constant in the same frequency range whenpatient has a larger fat mass (FIG. 10A). In addition, at the minimumpoint of phase, the magnitude of the frequency is different between thetwo patients.

FIG. 12 shows a correlation of muscle (MS) estimation by BIS and by MRI(MS_(BIS)=285*L²/Ri, where L (10 cm) is the distance between measuringelectrodes along the patient's calf and Ri is intracellular resistancewhich was calculated using the model of FIG. 2B). The value of 285 Ω-cmused as muscle resistivity in calculating MS_(BIS) was obtained by aregression analysis based on the MRI data.

In generating FIG. 12, for each patient, Ri was determined by solvingEquations 23-29 using the P₁, P₂, P₃, P₄, Q₁, Q₂, and Q₃ values obtainedfor that patient from the measured frequency response data. FIG. 12 thusillustrates the use of a group of parameters to quantify the analysis ofthe frequency response of the components of an equivalent circuit whichcan be used to identify the differences in body composition ofindividual subjects.

Differences in P₁, P₂, P₃, P₄, Q₁, Q₂, and Q₃ values were investigatedfor groups G1, G2, and G3 discussed above. Table 4 shows the significantdifference (p<0.05) of P₁ between G1 and G2 and the significantdifference of P₄ between G1 and G3. There were no significantdifferences except for P₁ and P₄ in the P and Q parameters.

Example 1 above showed that electrical resistivity of measurement on theskin surface is affected by adipose tissue using the equivalent circuitmodel of FIG. 2. This is believed to be one of the more importantfactors which influence the accuracy of bioimpedance technique toestimate body composition such as extracellular and intracellular fluidvolumes. Of course, bioimpedance accuracy is not only influenced by theamount of fat mass but also by the interface between electrodes and skinor the degree of skin hydration.

In this example, the results shown in FIG. 9 demonstrate a decrease inimpedance related to increase of the current frequency in patients withdifferent fat content. Impedance of the patient with larger fat mass ishigher than that of the patient with small fat mass. Simulation resultsof two patients with similar muscle mass and bone mass show that thefrequency response curve is different in the frequency range from 0 to 1kHz. The difference between FIGS. 10 and 11 demonstrate that the changein curve in response to the frequency from 0 to 1 kHz depends on the fatmass and that will largely affect the estimation of extracellular andintracellular resistance by multi-frequency bioimpedance analysis.Moreover, the difference at the minimum point of phase response betweenthe two patients indicates that using 50 kHz single frequencybioimpedance method could produce error when subject has a larger fatmass.

The correlation between muscle estimation by BIS and by MRI shown inFIG. 12 has a number of important implications for clinical and otherapplications. Thus, as illustrated in this figure, the electrical modelof the present invention correlates well with actual muscle mass asmeasured by MRI. The model therefore allows one to determine the musclemass of individual subjects (patients) using only simple, inexpensive,and non-invasive electrical measurements.

The particular muscle mass determined using the model will depend on theparticular locations chosen for the electrodes used to make the BISmeasurement. For example, the data of FIG. 12 is for the entire calfmuscle. By using a different electrode placement, the muscle mass of,for example, a portion of the calf muscle can be determined, e.g., themuscle mass of the gastrocnemius portion of the calf. Alternatively,rather than making measurements on the calf muscle, measurements can bemade on other muscles, portions of muscles, and/or or muscle groups,e.g., measurements can be made on all or part of a subject's biceps. Ifonly relative measurements are needed, the bioimpedance measurement canbe used as is. Alternatively, correlations of the type shown in FIG. 12can be obtained between bioimpedance measurements and MRI measurementsfor particular muscles, portions of muscles, or muscle groups, thusallowing the electrical measurements to provide “absolute” values formuscle mass, where “absolute” values are preferably those whichcorrespond to those obtained using MRI, the acknowledged “gold standard”for muscle mass measurements.

The ability to measure muscle mass, discrete muscles or muscle groupswith suitable application of electrodes, with or without validationagainst MRI measurements, has numerous applications. For example, thesetechniques are applicable in exercise programs in the home, gymnasium,sports and health clubs and in rehabilitation after surgery and injury,where the effect of muscle mass increases is relevant. Thus, by taking aseries of bioimpedance measurements over time, subjects (patients)and/or their health care professionals can monitor changes in musclemass as a result of exercise programs, diet changes, and/orrehabilitation programs.

Example 3 Single Low Frequency Bioimpedance Measurements

FIG. 13 is a plot based on the data of Examples 1 and 2 which shows thelack of a correlation between measured resistance values at 5 kilohertzand muscle mass determined by MRI. This data supports the conclusionthat at low frequencies, measured bioimpedance data is not responsive tothe muscle content of a segment. Rather, as set forth in the circuitmodel of FIG. 3, at these frequencies, the components of a segment thatprimarily determine the measured values obtained with a bioimpedanceprocedure are the fat and extracellular fluid components.

Example 4 Comparative Example Multi-Frequency, Three Parallel Path ModelVersus 50 Kilohertz

FIGS. 14 and 15 compare correlations between bioimpedance and MRImeasurements achieved using the multi-frequency, three parallel pathmodel of FIG. 2 with correlations achieved using impedance at a singlefrequency, namely, the commonly used frequency of 50 kilohertz. The dataused in preparing these figures was the data discussed above inconnection with Examples 1 and 2.

FIG. 14 shows muscle mass correlations, while FIG. 15 shows fat masscorrelations. As illustrated by these figures, the multi-frequency,three parallel path equivalent circuit frequency response model of theinvention achieves higher correlations than the single 50 kilohertzapproach both for muscle mass R² of 0.6 for the invention versus 0.3 for50 kilohertz) and for fat mass (R² of 0.7 for the invention versus 0.2for 50 kilohertz).

Example 5 Comparative Example Multi-Frequency, Three Parallel Path ModelVersus Cole-Cole Model

FIGS. 16 and 17 compare correlations between BIS and MRI measurementsachieved using the multi-frequency, three parallel path model of FIG. 2with correlations achieved using the Cole-Cole model. The data used inpreparing these figures was the data discussed above in connection withExamples 1 and 2.

FIG. 16 shows muscle mass correlations, while FIG. 17 shows fat masscorrelations. As illustrated by these figures, the multi-frequency,three parallel path equivalent circuit frequency response model of theinvention achieves higher correlations than the Cole-Cole model both formuscle mass (R² of 0.6 for the invention versus 0.4 for the Cole-Colemodel) and for fat mass (R² of 0.7 for the invention versus 0.1 for theCole-Cole model).

Although specific embodiments of the invention have been described andillustrated, it is to be understood that a variety of modificationswhich do not depart from the scope and spirit of the invention will beevident to persons of ordinary skill in the art from the foregoingdisclosure. As just one example, although the following claims recitevarious features of the invention, it is to be understood that theinvention encompasses any and all combinations of those features,irrespective of whether such combination is currently set forth in theappended set of claims.

REFERENCES

Citations for the various documents referred to above are set forthbelow. The contents of these documents are incorporated herein byreference.

-   [1] K. S. Cole and R. H. Cole, “Dispersion and absorption in    dielectrics. I. Alternating current characteristics” J. chem. Phys.    Vol. 9, pp. 341-351, 1941-   [2] H. P. Schwan, K. Li, “A dielectric study of the low-conductance    surface membrane,” in E. coli Nature Vol. 177, pp. 134-135, 1956-   [3] J. Nyboer, Electrical impedance plethysmography, 2^(nd) ed.,    Charles C. Thomas, Springfield, Ill. 1970-   [4] R. P. Patterson, “Fundamentals of impedance cardiography,” IEEE    Engineering in Medicine and Biology magazine. Vol. 8, pp. 16-18,    1989-   [5] T. Hanai, Electrical properties of emulsions In: Emulsion    Science, edited by P. H. Sherman London: Academic, 1968, pp.    354-477,-   [6] A. De Lorenzo, A. Andreoli, J. R. Matthie, and P. O. Withers,    “Predicting body cell mass with bioimpedance by using theoretical    methods: a technological review,” J Appl Physiol Vol. 82, pp.    1542-1558, 1997-   [7] R. N. Baumgartner, R. Ross and S. B. Heymsfield, “Does adipose    tissue influence bioelectric impedance in obese men and women?” J    Appl. Physiol. Vol. 84, pp. 257-262, 1998.-   [8] K. R. Foster and H. C. Lukaski, “Whole-body impedance—what does    it measure?” Am J Clin Nutr Vol. 64 (suppl), pp. 388S-396S, 1996-   [9] F. Zhu, S. Sarkar, C. Kaitwatcharachai, R. Greenwood, C.    Ronco, N. W. Levin, “Methods and reproducibility of measurement of    resistivity in the calf using regional bioimpedance analysis. Blood    Purif,” Vol. 21, pp. 131-136, 2003-   [10] Xitron Technologies, Inc., “4000B Bio-Impedance Spectrum    Analyzer System Operating Manual,” preliminary edition, San Diego,    Calif., 1995, Appendix A, pages 50-61.

TABLE 1 Permittivity Resistivity ε ρ (Ω-cm) Bone 640 10⁴ Fat 3 × 10⁴1.5~5 × 10³ Blood 2.8 × 10³   1.5 × 10² Muscle (parallel) 8 × 10⁴ 2 ×10²

TABLE 2 SUBJECT INFORMATION Mean SD min max SEX F9/M19 AGE, year 53.410.5 33 69 WEIGHT, kg 80.4 18 43.2 119.9 Height, cm 169.7 9.5 149 184.9BMI, kg/m2 27.7 4.97 19.18 41.11 FAT, g 344.9 118 149.2 533.5 MUSCLE, g525.3 110.3 326.5 761.5

TABLE 3 ρG, Mea ρ*G, Cal ρG, Cal Δρ VF/VG (Ω-cm) (Ω-cm) (Ω-cm)(Ω-cm) >0.2 430.4 ± 62 359.9 ± 43 457.2 ± 64 70.5 ± 24 =<0.2 369.5 ± 84322.7 ± 57 373.5 ± 70 46.8 ± 29 p value <0.05 n.s. <0.005 <0.05ρ_(G, Cal) and ρ*_(G, Cal) are the resistivity values calculated usingEq. 12 and Eq. 13, respectively; Δρ = ρ_(G, Mea) − ρ*_(G, Cal); a ρ_(E)value of 90 Ωcm was used in calculating ρ*_(G, Cal) and ρ_(G, Cal.)

TABLE 4 SUMMARY OF PARAMETERS FROM CURVE FITTING Fat P1 P2 P3 P4 Q1 Q2Q3 G1 32.54 ± 5.9 * 1412 ± 262 −15330 ± 3352 42640 ± 12130 ⁺ 22.5 ± 6.7−276.4 ± 76 649.8 ± 430 G2  27.3 ± 3.7 * 1187 ± 548 −13012 ± 3027 34166± 13808 22.6 ± 7.7   −262 ± 73   718 ± 372 G3   26 ± 4.4 1168 ± 259−10973 ± 3448 24191 ± 16426 ⁺ 20.7 ± 8.7 −197.2 ± 102 460.3 ± 460 * and⁺ indicate a significant (p < 0.05) difference between groups.

1. A method for analyzing bioimpedance data for a body segment of asubject, said body segment having an external skin surface, said methodcomprising: (a) applying alternating current at a plurality offrequencies to at least two points on the external skin surface so as tocause current to pass through the segment; (b) for each frequency,recording the voltage difference between at least two other points onthe external skin surface, said recorded voltage differences comprisingboth magnitude and phase information; and (c) using the recorded voltagedifferences at the plurality of frequencies to determine at least onenumerical value indicative of the muscle, fat, and/or extracellularfluid content of the segment, said numerical value being determinedusing an impedance model for the segment which at least comprises threeparallel paths, one of which consists of a capacitor C_(M) and aresistor R_(I) in series which represent primarily the muscle componentof the segment, one of which consists of a capacitor C_(F) and aresistor R_(F) in series which represent primarily the fat component ofthe segment, and one of which consists of a resistor; wherein the threeparallel path impedance model is used at least one frequency less thanor equal to 10 kilohertz and at least one frequency greater than 10kilohertz.
 2. The method of claim 1 wherein the at least one numericalvalue is indicative of the muscle content of the segment and is obtainedfrom a correlation equation which transforms an R_(I) value to a musclecontent value for the segment.
 3. The method of claim 2 wherein thecorrelation equation is obtained by: (i) performing steps (a), (b), and(c) on a plurality of calibration subjects to obtain an R_(I) value foreach of said subjects; (ii) performing magnetic resonance imaging of thesegment for the plurality of calibration subjects to obtain a value forthe muscle content of the segment for each of said subjects; and (iii)performing a regression analysis on the values obtained in steps (i) and(ii) to obtain the correlation equation.
 4. The method of claim 3wherein the regression analysis yields an R² value of at least 0.5 forthe correlation equation.
 5. The method of claim 4 wherein the pluralityof calibration subjects includes at least one calibration subject havinga body mass index less than 20 and at least one calibration subjecthaving a body mass index greater than
 35. 6. The method of claim 1wherein the at least one numerical value is indicative of the fatcontent of the segment and is obtained from a correlation equation whichtransforms an R_(F) value to a fat content value for the segment.
 7. Themethod of claim 6 wherein the correlation equation is obtained by: (i)performing steps (a), (b), and (c) on a plurality of calibrationsubjects to obtain an R_(F) value for each of said subjects; (ii)performing magnetic resonance imaging of the segment for the pluralityof calibration subjects to obtain a value for the fat content of thesegment for each of said subjects; and (iii) performing a regressionanalysis on the values obtained in steps (i) and (ii) to obtain thecorrelation equation.
 8. The method of claim 7 wherein the regressionanalysis yields an R² value of at least 0.5 for the correlationequation.
 9. The method of claim 8 wherein the plurality of calibrationsubjects includes at least one calibration subject having a body massindex less than 20 and at least one calibration subject having a bodymass index greater than
 35. 10. The method of claim 1 wherein theparallel path which consists of a resistor represents primarily theextracellular fluid component of the segment.
 11. The method of claim 1wherein the parallel path which consists of a resistor representsprimarily a parallel combination of the extracellular fluid and the bonecomponents of the segment.
 12. The method of claim 1 wherein theimpedance model further comprises a capacitor in series with the threeparallel paths.
 13. The method of claim 1 wherein the plurality offrequencies comprises frequencies greater than or equal to 5 kilohertzand less than or equal to 1000 kilohertz.
 14. The method of claim 1wherein the applied alternating currents of step (a) and the recordedvoltage differences of step (b) are used to calculate impedance valuesat the plurality of frequencies and step (c) comprises curve fitting tothose impedance values.
 15. The method of claim 14 wherein: (i) thecurve fitting employs an equation of the type:$Z_{Total} = \frac{{P_{1}\left( {j\;\varpi} \right)}^{3} + {P_{2}\left( {j\;\varpi} \right)}^{2} + {P_{3}\left( {j\;\varpi} \right)} + P_{4}}{\left( {j\;\varpi} \right)^{3} + {Q_{1}\left( {j\;\varpi} \right)}^{2} + {Q_{2}\left( {j\;\varpi} \right)} + Q_{3}}$where Z_(Total) is impedance, ω is angular frequency in radians persecond, j=√{square root over (−1)}, and P₁, P₂, P₃, P₄, Q₁, Q₂, and Q₃are group parameters which are a function of the electrical componentsemployed in the impedance model; and (ii) the P₁, P₂, P₃, P₄, Q₁, Q₂,and Q₃ values obtained for the subject from the curve fitting are usedto determine an R_(I) value and/or an R_(F) value for the subject. 16.The method of claim 1 wherein in step (a), said at least two points onthe external skin surface comprise: (i) two points on the subject's leg;(ii) two points on the subject's calf; (iii) two points on the subject'sarm; (iv) two points on the subject's biceps; (v) two points on thesubject's abdomen; (vi) one point on the subject's left hand and onepoint on the subject's right hand; (vii) one point on the subject's leftfoot and one point on the subject's right foot; or (viii) one point onone of the subject's hands or one of the subject's arms and one point onone of the subject's legs or one of the subject's feet.
 17. The methodof claim 1 further comprising displaying the at least one numericalvalue indicative of the muscle, fat, and/or extracellular fluid contentof the segment to a user.
 18. The method of claim 1 wherein the methodis performed on the same subject at two or more points in time.
 19. Themethod of claim 18 wherein the method is performed in connection with:(i) a dialysis procedure; (ii) an exercise program; (iii) arehabilitation program; and/or (iv) a weight control program. 20.Apparatus for analyzing bioimpedance data comprising a programmedcomputer for performing the method of claim 1.